Toward better understanding of the high-pressure structural transformation in beryllium by the statistical moment method.

Beryllium is a vital alkaline-earth metal for plasma physics, space science, and nuclear technology. Unfortunately, its accurate phase diagram is clouded by many controversial results, even though solid beryllium can only exist with hcp or bcc crystalline structures. Herein, we offer a simple quantum-statistical solution to the above problem. Our core idea is to develop the moment expansion technique to determine the Helmholtz free energy under extreme conditions. This strategy helps elucidate the underlying correlation among symmetric characteristics, vibrational excitations, and physical stabilities. In particular, our analyses reveal that the appearance of anharmonic effects forcefully straightens up the hcp-bcc boundary. This phenomenon explains why it has been difficult to detect bcc signatures via diamond-anvil-cell measurements. Besides, we modify the work-heat equivalence principle to quickly obtain the high-pressure melting profile from the room-temperature equation of state. The hcp-bcc-liquid triple point of beryllium is found at 165 GPa and 4559 K. Our theoretical findings agree excellently with cutting-edge ab initio simulations adopting the phonon quasiparticle method and the thermodynamic integration. Finally, we consider the principal Hugoniot curve and its secondary branches to explore the behaviors of beryllium under shock compression. Our predictions would be advantageous for designing inertial-confinement-fusion experiments.